Observed log-chlorophyll at representative station in SF Bay Delta region.
library(tidyverse)
library(lubridate)
library(mgcv)
library(plotly)
library(WRTDStidal)
library(gridExtra)
source('R/funcs.R')
# flow data, left moving window average of 30 days
data(flow_dat)
fl_dat <- flow_dat %>%
rename(date = Date) %>%
filter(station %in% 'sac') %>%
mutate(
qsm = stats::filter(q, rep(1, 30)/30, sides = 1, method = 'convolution')
)
# format the data to model
data(sf_dat)
sf_mod <- sf_dat %>%
filter(Site_Code %in% 'C3') %>%
rename(date = Date) %>%
mutate(
doy = yday(date),
dec_time = decimal_date(date),
yr = year(date),
mo = month(date, label = T)
) %>%
left_join(fl_dat, by = 'date') %>%
mutate(
flo = log(qsm),
lnchl = log(chl)
) %>%
select(-q, -qsm, -station, -Latitude, -Longitude, -Location)
# plot, all
p <- ggplot(sf_mod, aes(x = date, y = lnchl)) +
geom_line() +
theme_bw()
ggplotly(p)
# boxplot, by years
p <- ggplot(sf_mod, aes(x = yr, y = lnchl)) +
geom_boxplot() +
theme_bw()
ggplotly(p)
# boxplot, by month
p <- ggplot(sf_mod, aes(x = mo, y = lnchl)) +
geom_boxplot() +
theme_bw()
ggplotly(p)
Some simple GAMs to explore annual, seasonal trends.
# annual only
mod1 <- gam(lnchl ~ s(dec_time, bs = 'tp'),
data = sf_mod,
na.action = na.exclude
)
# seasonal only
mod2 <- gam(lnchl ~ s(doy, bs = 'cc'),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
# annual and seasonal, additive
mod3 <- gam(lnchl ~ s(dec_time, bs = 'tp') +
s(doy, bs = 'cc'),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
# annual and seasonal, interaction
mod4 <- gam(lnchl ~ te(dec_time, doy, bs = c('tp', 'cc')),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
Summary stats of annual, seasonal models:
mods <- list(
mod1 = mod1,
mod2 = mod2,
mod3 = mod3,
mod4 = mod4
)
# smoother stats of GAMs
map(mods, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable
| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| mod1 | s(dec_time) | 6.866894 | 7.962040 | 29.95751 | 0 |
| mod2 | s(doy) | 3.191626 | 8.000000 | 12.60039 | 0 |
| mod3 | s(dec_time) | 7.272455 | 8.281637 | 35.56688 | 0 |
| mod3 | s(doy) | 3.591968 | 8.000000 | 18.27905 | 0 |
| mod4 | te(dec_time,doy) | 13.362860 | 15.974582 | 27.26270 | 0 |
# summary stats of GAMs
map(mods, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
kable
| name | AIC | R2 |
|---|---|---|
| mod1 | 1117.9219 | 0.3025777 |
| mod2 | 1215.8161 | 0.1606211 |
| mod3 | 986.8771 | 0.4548302 |
| mod4 | 995.0956 | 0.4490483 |
# prediction data
pred_dat <- data.frame(
dec_time = seq(min(sf_mod$dec_time), max(sf_mod$dec_time), length = 1000)
) %>%
mutate(
date = date_decimal(dec_time),
date = as.Date(date),
mo = month(date, label = TRUE),
doy = yday(date),
yr = year(date)
) %>%
left_join(., fl_dat[, c('date', 'qsm')]) %>%
mutate(flo = log(qsm)) %>%
select(-qsm)
# predictions
sf_res <- pred_dat %>%
mutate(
mod1 = predict(mod1, newdata = pred_dat),
mod2 = predict(mod2, newdata = pred_dat),
mod3 = predict(mod3, newdata = pred_dat),
mod4 = predict(mod4, newdata = pred_dat)
) %>%
tidyr::gather('mods', 'pred', -date, -mo, -doy, -dec_time, -yr, -flo)
# plot
p <- ggplot(sf_res, aes(x = date)) +
geom_point(data = sf_mod, aes(y = lnchl), size = 0.5) +
geom_line(aes(y = pred, colour = mods)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
)
ggplotly(p)
# plot
p <- ggplot(sf_res, aes(x = doy, group = factor(yr), colour = yr)) +
geom_line(aes(y = pred)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
) +
facet_wrap(~ mods, ncol = 2)
ggplotly(p)
Adding flow data to the model:
# model, all terms additive
mod5 <- gam(lnchl ~ s(dec_time, bs = 'tp') + s(doy, bs = 'cc') + s(flo, bs = 'tp'),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
# model, flo additive, interaction between dec_time, doy
mod6 <- gam(lnchl ~ te(dec_time, doy, bs = c('tp', 'cc')) + s(flo, bs = 'tp'),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
# model, doy additive, interaction between dec_time and flow
mod7 <- gam(lnchl ~ te(dec_time, flo, bs = c('tp', 'tp')) + s(doy, bs = 'cc'),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
# model, dec_time additive, interaction between flo and doy
mod8 <- gam(lnchl ~ te(flo, doy, bs = c('tp', 'cc')) + s(dec_time, bs = 'tp'),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
# model, interaction between flow and doy, interaction between flo and dec_time
mod9 <- gam(lnchl ~ te(flo, doy, bs = c('tp', 'cc')) + te(flo, dec_time, bs = c('tp', 'tp')),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
# model, all terms interaction
mod10 <- gam(lnchl ~ te(dec_time, doy, flo, bs = c('tp', 'cc', 'tp')),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
Summary stats of annual, seasonal, flow models:
mods2 <- list(
mod5 = mod5,
mod6 = mod6,
mod7 = mod7,
mod8 = mod8,
mod9 = mod9,
mod10 = mod10
)
# smoother stats of GAMs
map(mods2, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable
| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| mod5 | s(dec_time) | 7.369642 | 8.356655 | 31.480016 | 0 |
| mod5 | s(doy) | 3.367204 | 8.000000 | 20.930200 | 0 |
| mod5 | s(flo) | 7.455219 | 8.426530 | 7.472015 | 0 |
| mod6 | te(dec_time,doy) | 13.543810 | 16.196276 | 26.290240 | 0 |
| mod6 | s(flo) | 7.369249 | 8.366403 | 7.627124 | 0 |
| mod7 | te(dec_time,flo) | 15.242514 | 18.208885 | 23.349565 | 0 |
| mod7 | s(doy) | 3.668998 | 8.000000 | 22.815999 | 0 |
| mod8 | te(flo,doy) | 18.256992 | 18.843439 | 12.894742 | 0 |
| mod8 | s(dec_time) | 7.384604 | 8.369949 | 32.857922 | 0 |
| mod9 | te(flo,doy) | 13.660332 | 15.634178 | 17.353062 | 0 |
| mod9 | te(flo,dec_time) | 14.432207 | 20.000000 | 16.366477 | 0 |
| mod10 | te(dec_time,doy,flo) | 45.650084 | 57.598811 | 12.305912 | 0 |
# summary stats of GAMs
map(mods2, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
kable
| name | AIC | R2 |
|---|---|---|
| mod5 | 934.8386 | 0.5106123 |
| mod6 | 941.7425 | 0.5067670 |
| mod7 | 912.1389 | 0.5310632 |
| mod8 | 941.6199 | 0.5109185 |
| mod9 | 925.8831 | 0.5267709 |
| mod10 | 896.0992 | 0.5649017 |
# predictions
sf_res2 <- pred_dat %>%
mutate(
mod5 = predict(mod5, newdata = pred_dat),
mod6 = predict(mod6, newdata = pred_dat),
mod7 = predict(mod7, newdata = pred_dat),
mod8 = predict(mod8, newdata = pred_dat),
mod9 = predict(mod9, newdata = pred_dat),
mod10 = predict(mod10, newdata = pred_dat)
) %>%
tidyr::gather('mods', 'pred', -date, -mo, -doy, -dec_time, -yr, -flo)
# plot
p <- ggplot(sf_res2, aes(x = date)) +
geom_point(data = sf_mod, aes(y = lnchl), size = 0.5) +
geom_line(aes(y = pred, colour = mods)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
)
ggplotly(p)
ptheme <- theme(
axis.title.x = element_blank(),
axis.title.y = element_blank()
)
cols <- 'Spectral'
p5 <- dynagam(mod5, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
theme(legend.position = 'none') +
ggtitle('mod5')
p6 <- dynagam(mod6, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
theme(legend.position = 'none') +
ggtitle('mod6')
p7 <- dynagam(mod7, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
theme(legend.position = 'none') +
ggtitle('mod7')
p8 <- dynagam(mod8, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
theme(legend.position = 'none') +
ggtitle('mod8')
p9 <- dynagam(mod9, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
theme(legend.position = 'none') +
ggtitle('mod9')
p10 <- dynagam(mod10, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
ggtitle('mod10')
pleg <- g_legend(p10)
p10 <- p10 +
theme(legend.position = 'none')
grid.arrange(
pleg,
arrangeGrob(p5, p6, p7, p8, p9, p10, ncol = 6, bottom = 'lnQ', left = 'lnchl'),
ncol = 1,
heights = c(0.1, 1)
)
Backwards model selection, see here:
mod <- gam(lnchl ~ s(dec_time, bs = 'tp') +
s(doy, bs = 'cc') +
s(flo, bs = 'tp') +
te(flo, doy, bs = c('tp', 'cc')) +
te(flo, dec_time, bs = c('tp', 'tp')) +
te(dec_time, doy, bs = c('tp', 'cc')) +
te(dec_time, doy, flo, bs = c('tp', 'cc', 'tp')),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
summary(mod)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## lnchl ~ s(dec_time, bs = "tp") + s(doy, bs = "cc") + s(flo, bs = "tp") +
## te(flo, doy, bs = c("tp", "cc")) + te(flo, dec_time, bs = c("tp",
## "tp")) + te(dec_time, doy, bs = c("tp", "cc")) + te(dec_time,
## doy, flo, bs = c("tp", "cc", "tp"))
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.61252 0.02209 27.73 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(dec_time) 6.339e+00 7.475 2.969 0.003902 **
## s(doy) 1.864e+00 8.000 0.356 0.053668 .
## s(flo) 6.562e+00 7.697 1.548 0.175616
## te(flo,doy) 6.260e+00 15.000 1.421 7.89e-05 ***
## te(flo,dec_time) 7.989e+00 16.000 2.972 8.72e-10 ***
## te(dec_time,doy) 7.706e+00 15.000 1.576 0.000341 ***
## te(dec_time,doy,flo) 3.457e-08 48.000 0.000 0.201552
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.578 Deviance explained = 60.7%
## GCV = 0.28725 Scale est. = 0.26748 n = 548
AIC(mod)
## [1] 870.8656
mod <- gam(lnchl ~ s(dec_time, bs = 'tp') +
s(doy, bs = 'cc') +
s(flo, bs = 'tp') +
te(flo, doy, bs = c('tp', 'cc')) +
te(flo, dec_time, bs = c('tp', 'tp')) +
te(dec_time, doy, bs = c('tp', 'cc')),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
summary(mod)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## lnchl ~ s(dec_time, bs = "tp") + s(doy, bs = "cc") + s(flo, bs = "tp") +
## te(flo, doy, bs = c("tp", "cc")) + te(flo, dec_time, bs = c("tp",
## "tp")) + te(dec_time, doy, bs = c("tp", "cc"))
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.61252 0.02209 27.73 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(dec_time) 6.339 7.475 2.969 0.003902 **
## s(doy) 1.864 8.000 0.356 0.053668 .
## s(flo) 6.562 7.697 1.548 0.175616
## te(flo,doy) 6.260 15.000 1.421 7.89e-05 ***
## te(flo,dec_time) 7.989 16.000 2.972 8.72e-10 ***
## te(dec_time,doy) 7.706 15.000 1.576 0.000341 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.578 Deviance explained = 60.7%
## GCV = 0.28725 Scale est. = 0.26748 n = 548
AIC(mod)
## [1] 870.8656
mod <- gam(lnchl ~ s(dec_time, bs = 'tp') +
s(doy, bs = 'cc') +
te(flo, doy, bs = c('tp', 'cc')) +
te(flo, dec_time, bs = c('tp', 'tp')) +
te(dec_time, doy, bs = c('tp', 'cc')),
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
summary(mod)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## lnchl ~ s(dec_time, bs = "tp") + s(doy, bs = "cc") + te(flo,
## doy, bs = c("tp", "cc")) + te(flo, dec_time, bs = c("tp",
## "tp")) + te(dec_time, doy, bs = c("tp", "cc"))
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.61252 0.02226 27.52 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(dec_time) 6.428 7.562 4.517 5.08e-05 ***
## s(doy) 3.846 8.000 1.711 6.34e-05 ***
## te(flo,doy) 10.174 12.014 2.876 0.000673 ***
## te(flo,dec_time) 8.206 16.000 3.929 4.44e-13 ***
## te(dec_time,doy) 8.612 12.000 1.789 0.002231 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.572 Deviance explained = 60.1%
## GCV = 0.29193 Scale est. = 0.27154 n = 548
AIC(mod)
## [1] 879.6259